Hamilton-Jacobi theory in multisymplectic classical field theories

Abstract

The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.

44 pp

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Cited by in corpus (5)

• Reviewing the Geometric Hamilton-Jacobi Theory concerning Jacobi and Leibniz identities
• Geometric Hamilton-Jacobi theory for systems with external forces
• An overview of the Hamilton--Jacobi theory: the classical and geometrical approaches and some extensions and applications
• Hamilton-Jacobi theory for gauge field theories
• Variational Principles for Hamiltonian Systems